About 25,000 people were in the area at the time but they left calmly shortly before 2100 local time (1900 GMT), a police officer said.
The 324m (1,063ft) iron lattice tower, built in 1889, is one of the world’s most popular tourist attractions.
Those evacuated were moved to the banks of the nearby River Seine.
Police with sniffer dogs are carrying out a search of the area, French media reported.
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